Phasor-I1 Grid Following Voltage Source Converter
Reviewers: Eduardo Prieto Araujo (UPC), Josep Fanals Batllori (eRoots)
Context
The Phasor-\(I_1\) Grid Following Voltage Source Converter (VSC) model [1] is derived from the Full-Phasor.
Model use, assumptions, validity domain and limitations
The model can be used to fasten the simulations for low-frequency phenomena studies. If the simulation step size is desired to be close to the dynamics of the current control loop (around \(10^3\) \(\mu s\)), the Phasor-\(I_1\) model performs better than the Full-Phasor model, which will have an important increase of the error (or even divergence) when using these step sizes.
The assumptions made starting from the Full-Phasor model are the following:
- The current loop is substituted by a first-order transfer function with a given time constant.
The model shows a performance close to more accurate models during for slow dynamics such as setpoint tracking or voltage/frequency deviation. It can solve high frequency phenomena with clear limitations, as the results do not capture correctly the dynamics of phenomena like asymmetrical faults.
Although it allows a bigger time step than the Full-Phasor model, it eventually will diverge if it is increased too much, as it still retains some dynamics in an approximate way. The Phasor-\(I_0\) model is more suitable as it completely removes the current loop dynamics.
Model description
The diagram of the complete model is shown in the following figure.
The following subsections will describe the changes with respect to the Full-Phasor model.
Current loop
The differential equations that modelled the behavior of the current loop are substituted by a first-order transfer function with a given time constant:
where \(\tau_c = \frac{1}{w_c}\) is the time constant of the current loop, being \(w_c\) the frequency that is set to match the bandwidth of the original current loop.
Outer loop
No changes are made directly to this outer-loop, although the time constant \(\tau_c\) will act as a low-pass filter of the current setpoint provided by the outer loop.
Open-source implementations
No open-source implementations have been found.
Table of references
[1] Lacerda, V. A.; Prieto-Araujo, E.; Cheah, M.; Gomis-Bellmunt, O. “Phasor Modeling Approaches and Simulation Guidelines of Voltage-Source Converters in Grid-Integration Studies”, May 2022, IEEE Access, DOI: 10.1109/ACCESS.2022.3174958
[2] Lacerda, V. A.; Prieto-Araujo, E.; Cheah, M.; Gomis-Bellmunt, O. “Phasor and EMT models of grid-following and grid-forming converters for short-circuit simulations.”, October 2023, vol. 223, núm. 109662. DOI: 10.1016/j.epsr.2023.109662
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